AJAX numerical pagination problem in TwentyFifteen-child theme

Have you checked with js Console that the ajax returned the expected data[‘html’]?

The url you show after the second page click attempt has /admin-ajax.php/ inside it. That shouldn’t happen. It’s a good indicator that the ajax transfer or the returned output/query is at some point broken.

Would have been useful, if you also show the relevant html parts. Without it we can’t check whether the page = find_page_number( $(this).clone() ); is a proper and best-practice function.

To me it seems the $GLOBALS['wp_query'] = $posts; can be also problematic part.
Why do you need to modify globals directly? It’s not the common/best practice as i know.

I recommend this well detailed explanation on WP Query types and their proper usage for everyone, who feels not 110% familiar with the WP query-system.

(p.s.: have you managed to solve this problem several months back then? Maybe to answer on your own question or make an Update would be useful for others, in case you solved this issue. Cheers)